Efimov States of Three Unequal Bosons in Non-integer Dimensions

Christensen, E.R.; Jensen, A. S.; Garrido, E.

doi:10.1007/s00601-018-1457-9

Cited by 15 publications

(15 citation statements)

References 14 publications

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“…We still need much more studies to understand what is the physical meaning of a fractional D in Efimov states. Besides we have already some estimates on how the effective dimension changes according to the oscillator parameter [1,16] a direct relation of D with some trap parameter should still be found.…”

Section: Resultsmentioning

confidence: 99%

Dimensional Effects in Efimov Physics

Yamashita

2019

Few-Body Syst

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Efimov physics is drastically affected by the change of spatial dimensions. Efimov states occur in a tridimensional (3D) environment, but disappear in two (2D) and one (1D) dimensions. In this paper, dedicated to the memory of Prof. Faddeev, we will review some recent theoretical advances related to the effect of dimensionality in the Efimov phenomenon considering three-boson systems interacting by a zero-range potential. We will start with a very ideal case with no physical scales [1], passing to a system with finite energies in the Born-Oppenheimer (BO) approximation [2] and finishing with a general system [3]. The physical reason for the appearance of the Efimov effect is given essentially by two reasons which can be revealed by the BO approximation -the form of the effective potential is proportional to 1/R 2 (R is the relative distance between the heavy particles) and its strength is smaller than the critical value given by −(D − 2) 2 /4, where D is the effective dimension.

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Section: Resultsmentioning

confidence: 99%

Dimensional Effects in Efimov Physics

Yamashita

2019

Few-Body Syst

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“…Our starting point is Eq. ( 8) and the two-body T-matrix (33) for a 0 = ±∞. We are assuming that the subsystem AA has two channels and AB has only one open channel.…”

Section: Modelmentioning

confidence: 99%

“…However, it still missing systematic experimental studies about the effect of the dimensional change in few-body observables, e.g., the Efimov effect is drastically affected by the spatial dimensional reduction. The disappearance of Efimov effect in fractional dimensions between three and two dimensions, including another few-body aspects involving a continuous change of spatial dimensions, has recently being investigated by some groups [26,[30][31][32][33][34][35][36].…”

Section: Introduction -An Overview Of Recent Problems Involving Universality In Few-body Systemsmentioning

confidence: 99%

Emergence of N-Body Tunable Interactions in Universal Few-Atom Systems

2020

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A three-atom molecule AAB, formed by two identical bosons A and a distinct one B, is studied by considering coupled channels close to a Feshbach resonance. It is assumed that the subsystems AB and AA have, respectively, one and two channels, where, in this case, AA has open and closed channels separated by an energy gap. The induced three-body interaction appearing in the single channel description is derived using the Feshbach projection operators for the open and closed channels. An effective three-body interaction is revealed in the limit where the trap setup is tuned to vanishing scattering lengths. The corresponding homogeneous coupled Faddeev integral equations are derived in the unitarity limit. The s-wave transition matrix for the AA subsystem is obtained with a zero-range potential by a subtractive renormalization scheme with the introduction of two finite parameters, besides the energy gap. The effect of the coupling between the channels in the coupled equations is identified with the energy gap, which essentially provides an ultraviolet scale that competes with the van der Waals radius-this sets the short-range physics of the system in the open channel. The competition occurring at short distances exemplifies the violation of the "van der Waals universality" for narrow Feshbach resonances in cold atomic setups. In this sense, the active role of the energy gap drives the short-range three-body physics.

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“…One spectacular prediction was that the Efimov effect is only possible in dimensions between 2.3 and 3.8. This dmethod was recently implemented to investigate the confinement of two-and three-body systems [31][32][33][34]. Practical calculations for non-integer dimensions are precisely as easy, or difficult, as in the usual 3D-space.…”

mentioning

confidence: 99%

“…This limit translates into ω ho < 1.02ω pp , which means that a larger squeezing frequency than 1.02ω pp cannot produce an Efimov effect for three identical bosons. For one light and two identical heavy particles the limit value can move up or down depending on the mass ratio, as shown in [32].…”

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confidence: 99%

Efimov effect in non-integer dimensions induced by an external field

Garrido,

Jensen

2020

Preprint

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The Efimov effect can be induced by means of an external deformed one-body field that effectively reduces the allowed spatial dimensions to less than three. To understand this new mechanism, conceptually and practically, we employ a formulation using non-integer dimension, which is equivalent to the strength of an external oscillator field. The effect most clearly appears when the crucial twobody systems are unbound in three, but bound in two, dimensions. We discuss energy variation, conditions for occurrence, and number of Efimov states, as functions of the dimension. We use practical examples from cold atomic physics of 133 Cs-133 Cs-133 Cs, 87 Rb-87 Rb-87 Rb, 133 Cs-133 Cs-6 Li, and 87 Rb-87 Rb-39 K. Laboratory tests of the effect can be performed with two independent parameters, i.e. the external one-body field and the Feshbach two-body tuning. The scaling and (dis)appearance of these Efimov states are precisely as established in three dimensions.

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Efimov States of Three Unequal Bosons in Non-integer Dimensions

Cited by 15 publications

References 14 publications

Dimensional Effects in Efimov Physics

Dimensional Effects in Efimov Physics

Emergence of N-Body Tunable Interactions in Universal Few-Atom Systems

Efimov effect in non-integer dimensions induced by an external field

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